The generation of strong and homogeneous magnetic fields is of great interest in many technical applications. In particular, it is very important for clinical magnetic resonance imaging (MRI). Many of the early magnet designs were based on the work of Garrett [1,2]. The central uniformity of symmetrical fields was analyzed by a spherical harmonic expansion. There is only a small body of literature available on the design of superconducting main magnets for these systems. In recent years, there has been an increasing interest in optimal design of clinical MRI magnets. Pissanetzky [3] has proposed an approach to field design based on a hybrid methodology incorporating ideas from finite elements, analytical techniques, and other numerical methods. Thompson [4] has illustrated a method based on a variational approach with constraints introduced by Lagrange multipliers. The analytical aspects of variational calculus were combined with numerical techniques to obtain optimal spatial coil distributions. Crozier [5] has introduced a stochastic optimization technique that was successfully used to design compact MRI magnets. Zhao [6, 7, 8] has used an inverse approach to formulating a continuous function space for solution and then used integration relationships to define a kernel matrix linear equation. The problem has then been solved as a nonlinear optimization.
In general, the design of a superconducting MRI magnet requires the consideration of various parameters. These include: central magnetic field strength, spatial homogeneity, peak field in the superconductors, size of stray field, stress in the superconductor coil, geometrical constraints, weight and cost. For clinical imaging, these constraints include:                there is a specific volume of interest (SVOI) of sufficient size such that the field homogeneity in this region encapsulates the sample to be imaged;        for clinical imaging, the SVOI must be sufficiently large to be able to cover the defined region of interest of the human body. In general VSVOI≧5×104 cm3 but lesser volumes are acceptable depending on the application.        the inhomogeneity of the static fields in the SVOI are usually constrained to be less than 10 parts per million (ppm);        the field strength should as strong as possible, stable, with a drift of a few Hertz per hour and in general, for high resolution imaging, B0≧1.5 T. Within a target design, there are practical and physical constraints that set the upper bound for the field.        the stray field region should be as small as possible to allow the magnet to be sited in the smallest possible space. Critically, the magnet must not effect any auxiliary equipment and cannot pose a risk to humans fitted with pacemakers.        in closed systems, the magnet inner clear bore diameter (often referred to as the warm bore diameter) should be sufficiently large to allow the patient or part of the patient being imaged to comfortably completely fit within the magnet;        consistent with the physics of the problem and the cost drivers in magnet manufacture, the magnet length should be as short as possible to reduce claustrophobia in patients;        a superconducting magnet should be safe, e.g. operate under stable engineering conditions and have a very high quench threshold;        the current density and the field in the superconductor wire should operate within an appropriate safety margin to protect the magnet from quenching;        the magnet subsystem, coil bundles, formers and cryostat must be capable of withstanding the stress induced by Lorentz's force without damage, and if a quench does occur the magnet is not destroyed.        
The challenge in designing a high field compact magnet is the retention of high homogeneity conditions over the imaging volume while maintaining all the other requirements. As magnet performance is strongly dependent on the overall length and the inner diameter of the coil structure, the shorter the length and the larger the inner diameter of the magnet, the more difficult it is to maintain the homogeneity specification. For a clinical MRI superconductor magnet, the advantages of a shorter magnet with a stronger field are very clear, but it is also important that image quality should not be compromised by making the magnet shorter. The main advantages of making the magnet shorter and with a larger diameter include the potential to reduce the perception of claustrophobia for the patient and better access to the patient by attending physicians. However, as the magnet length becomes shorter and as its central field increases, the degree of difficulty in designing and producing such a magnet significantly increases.
The successful design and construction of a superconducting magnet is a three stage process. First, a theoretical design is produced which optimizes field homogeneity over the region of interest, minimizes the stress on the coils and the coil formers, and minimizes cost. This invention concerns this first step. In a second step, working drawings are developed and the magnet is wound with the whole assembly, coils, formers and cryostat at room temperature. The third step involves cooling the assembly to liquid helium temperatures. During this last step the component parts will contract to the extent that the calculated homogeneity predicted by the first step will not be achieved. Often errors in the order of many hundreds of ppm are induced by the winding process (at room temperature) and additional thermal and subsequent stresses are induced by cooling to 4K and charging the magnet to the required field.
The design of a superconducting magnetic resonance imaging (MRI) magnet is a very specific problem because of one essential feature: virtually every characteristic parameter of the field produced is determined by the geometry of the current-bearing superconductors. Various methods are used to overcome the mathematical and computational difficulty to obtain a homogeneous magnetic field over a SVOI, control of the maximum peak field inside the superconductors, limit leakage magnetic field and keep the stress in a wire bundle within a certain level. The main cost driver is the type and amount of the superconductor wire used.
U.S. Pat. No. 5,818,319 describes a magnet for a magnetic resonance system and a procedure for the designing that magnet. The method is appropriate for the design of superconducting magnets, shim magnets and gradient magnets for magnetic resonance. A simulated annealing procedure is used in the procedure error function having weighted spherical harmonics. The optimizing procedure results in a superconducting magnet having at least one coil with current flowing in an opposite direction to that of adjoining coils. The reverse current flow in combination with the relatively large number of coils, e.g. more than six, leads to the development of short, homogenous whole body magnets for magnetic resonance imaging. The patent discloses a homogenous volume of 40×103 cm3 and emphasizes design of a magnet having one single primary coil layer and one single shielding layer.
The U.S. Pat. No. 5,818,319 patent is prescriptive in the length of the magnet to be designed. For some applications the art described in the '319 patent may not lead to a design for the application being considered because the stress in coil bundles may be outside acceptable design limits.
In view of the above it is the purpose of the present invention to present a superconducting magnet design appropriate for use in MRI which permits an extremely compact magnet construction with sufficiently large investigational volumes of appropriate homogeneity to permit investigation of the human anatomy, while nevertheless maintaining a coil structure of sufficient strength to satisfy safety requirements as well as to prevent quenching of the magnet.